An Optimal Inspection and Replacement Policy

An optimal inspection and replacement policy is discussed for a unit which assumes any one of several Markov states. The policy evaluation function is the s-expected cost-per-unit-time over an infinite time span. The problem is formulated as a semi-Markov decision process with a modified policy-improvement routine. Some properties of the optimal policy are discussed, for example, the control limit rule holds and the inspection time interval becomes shorter as degradation progresses.